Simulation of thermal processes in the lining of the ship's boiler

Судовой котлоагрегат подвергается воздействиям высокого давления рабочего тела и температуры дымовых газов. Кроме того работа его осложняется также быстрой и частой сменой нагрузки. Для продолжительной и надёжной работы котлов необходимо обеспечить прочность их конструкций, в частности, футеровки. Судовые котельные агрегаты футеруются огнеупорными материалами, во многом определяющими срок службы котла. При тепловом воздействии на теплоизоляционные материалы футеровки возникают термические напряжения, приводящие к деформации, растрескиванию и разрушению кирпичной кладки. Однако ввиду сложности постановки прямого физического эксперимента пока нет однозначного ответа на вопрос, какие условия способствуют разрушительному тепловому воздействию на футеровку котла. Потому авторы предлагают исследовать тепловые процессы в кирпичной кладке методами математического моделирования. В прикладном пакете ANSYS R17.2 WORKBENCH была создана твердотельная модель элемента футеровки (кирпича), на которой исследовались стационарные и нестационарные процессы теплообмена с граничными условиями первого и третьего рода. В результате экспериментов установлено, что разность деформаций соседних слоев огнеупора пропорциональна градиенту температуры, причём в нестационарных режимах теплообмена величина температурного градиента может значительно превышать его значение в стационарных условиях. Если учесть, что при форсированной нагрузке температура дымовых газов в топочном объёме достигает предельных значений, а интенсивность конвективного теплообмена существенно возрастает, то температурные напряжения, возникающие в футеровке котла, могут превысить предел прочности огнеупора. The ship's boiler unit is exposed to the high pressure of the working fluid and the temperature of the flue gases. The operating conditions are aggravated with rapid and frequent alternations in load. To ensure continuous and reliable operation, boiler and its elements, including lining, design needs to be strong. Ship boilers are lined with fire resistant materials, which lining basically defines lifetime of a boiler. Any heat impact to lining insulation will result in thermal stress that leads to deformation, cracking and destruction of brickwork. However, as direct physical experiment is difficult to conduct, there has been no clear understanding as to what conditions cause destructive thermal impact to the boiler lining. In light of this, the authors propose to investigate thermal processes in brickwork by mathematical modeling methods. Using ANSYS R17.2 WORKBENCH application package, the solid model of the lining element (brick) was created and stationary and non-stationary heat exchange processes with the boundary conditions of the first and third order were investigated. The experiments showed that the difference of deformations of neighboring lining layers was proportional to temperature gradient, yet in non-stationary heat exchange mode the temperature gradient can be significantly higher than that in stationary conditions. Considering that in forced loading mode the temperature of flue gases in boiler furnace can reach its limit and intensity of convective heat exchange increases significantly, the temperature stress that occurs in the boiler lining can exceed the strength of fire resistant brickwork.

An Extended Analytical Solution of the Non-Stationary Heat Conduction Problem in Multi-Track Thick-Walled Products during the Additive Manufacturing Process

An analytical model has been developed for calculating three-dimensional transient temperature fields arising in the direct deposition process to study the thermal behavior of multi-track walls with various configurations. The model allows the calculation of all characteristics of the temperature fields (thermal cycles, cooling rates, temperature gradients) in the wall during the direct deposition process at any time. The solution of the non-stationary heat conduction equation for a moving heat source is used to determine the temperature field in the deposited wall, taking into account heat transfer to the environment. The method considers the size of the wall and the substrate, the change in power from layer to layer, the change in the cladding speed, the interpass dwell time (pause time), and the heat source trajectory. Experiments on the deposition of multi-track block samples are carried out, as a result of which the values of the temperatures are obtained at fixed points. The proposed model makes it possible to reproduce temperature fields at various values of the technological process parameters. It is confirmed by comparisons with experimental thermocouple data. The relative difference in the interlayer temperature does not exceed 15%.

Influence of extended heat sources on the temperature distribution in profiled polar-orthotropic annular plates with heat-insulated bases

The solution of the stationary heat conduction problem for profiled polar-orthotropic annular plates with heat-insulated bases from N extended heat sources at their external border is presented. The temperature distribution in such plates will be non-axisymmetric. The solution of the stationary heat conduction problem for anisotropic annular plates of an random profile is resolved through the solution of the corresponding Volterra integral equation of the second kind. The formula of a temperature calculations in anisotropic annular plates of an random profile is given. The exact solution of stationary heat conduction problem for polar-orthotropic annular plate of an exponential profile is recorded. The temperature distribution in such anisotropic plate from N extended heat sources at its outer border is more complex than in the case of temperature distribution from N point heat sources at their external border.

Estimation of a Thermal Conductivity in a Stationary Heat Transfer Problem with a Solid-Solid Interface

An inverse problem for a stationary heat transfer process is studied for a totally isolated bar on its lateral surface, made up of two consecutive sections of different, isotropic and homogeneous materials, perfectly assembly, where one of the materials, that is unreachable and unknown, has to be identified. The length of the bar is assumed to be much greater that the diameter so that a 1D heat transfer process is considered. A constant temperature is assumed at the end of the unknown part of the rod while the other end is let free for convection. We propose a procedure to identify the unknown material of the bar based on a noisy flow measurement at the opposite end. Necessary and sufficient conditions are derived together with a bound for the estimation error. Moreover, elasticity analysis is performed to study the influence of the data in the conductivity estimation and numerical examples are included to illustrate the proposed ideas and show the estimation performance.

MATHEMATICAL MODELLING OF NON-STATIONARY HEAT TRANSFER IN A MULTILAYER COMPOSITE MATERIAL

The article considers the issue of designing a composite textile material based on the use of a 3D textile matrix for firefighter combat clothing with improved performance characteristics. To reduce labour and material costs for design and create an alternative to the experimental selection of the structure and composition of the material, a mathematical model of non-stationary heat transfer in the “environment – composite material – human” system is proposed. The problem of temperature distribution at any time for the outer and inner layers is presented in the form of heat transfer in a multilayer plate. The problem of temperature distribution in the heat-insulating layer of the material is presented in the form of heat transfer through a limited rod in the air. The developed mathematical model allows calculating the distribution of temperature fields in the layers of the material at different values of the effective heat flow and determine the limit parameters of its thermal protection effect.

STUDY OF ENERGY-SAVING LIQUID THERMAL INSULATING COATINGS BASED ON LOCAL FINELY DISPERSED SYSTEMS

Introduction: In recent years, in building materials science, there has been a tendency for the active introduction of hollow microspheres of various types for modifying the properties of building materials. Hollow microspheres are most widely used in the production of liquid thermal insulating coatings, which reduce heat loss, protect structures from corrosion and overheating, prevent condensation formation, reduce operating costs and increase the time between repairs. Aim: Assessment of the influence of the structural characteristics of granular systems on the properties of thermal insulating materials. Methods: It is proposed to determine and evaluate the structural characteristics of filler powders by the method of small-angle X-ray scattering. The most important feature of this method is analyzing the internal structure of disordered systems - particles, pore space, interfaces between heterogeneities of heterogeneous substances. When assessing thermal conductivity and thermal resistance, the stationary heat flux method was used following GOST 30290–94. The essence of the method is to create a stationary heat flux passing through a flat sample of a certain thickness and directed perpendicular to the front (largest) faces of the sample, measuring the density of this heat flux, the temperature of the opposite front faces and the thickness of the sample. Results and Discussion: The paper discusses the results of experimental studies that make it possible to create liquid thermal insulation coatings (LTIC) based on polymer binders, fine mineral powders, and a complex of modifying additives. Experimental studies of the structure and properties of heat-insulating coatings based on filled polymer binders confirm their superiority over foreign analogs. Conclusions: It has been established that during the production of LTIC, their heat-shielding properties can be regulated by changing: pressure, the viscosity of the molecular weight of the gas; porosity of macrostructure and clusters; the thermal conductivity of the solid and gas phase of the system; the coefficient of accommodation; coordination number; primary particle size; fractal dimension characterizing the topological features of the structure of particles, aggregates, globules, clusters and their tendency to dissipate the energy of gas molecules.

Calculation of non-stationary heat exchange in multi-layer media by means of the theory of Markov chains

Calculation of non-stationary heat exchange in multi-layer dissimilar media is the problem, which is often found in many industries including high temperature metallurgic technologies of production and treatment of metals, alloys and their products. The similar problems arise during the design of buildings and structures. The models used for calculation are mainly based on approximate solutions of classical heat conduction equations. The drawback of such models is a complex computational procedure, associated with the need to solve a large number of equations and to define a large number of identification parameters. At present, the calculation of one mode of heat transfer between the sections of a composite structure requires 6–8 hours of operation of a computer of average power. In this regard, the development of discrete models that require less computer time is of current importance. The proposed model of the process is based on the theory of Markov chains. A multi-layer medium is presented as a chain of small but finite cells. Each of them contains a certain amount of heat that can be transferred to the neighboring cells. The part of the transferred heat is directly proportional to the heat conduction coefficient and in inverse proportion to the material heat capacity, material density and the cell length. The matrix model to describe heat transfer between cell in a multi-layer media based on the theory of Markov chains is developed. Construction of the matrix of transition probabilities is described, evolution of the state vectors i.e. distribution of heat and temperature is carried out, and non-uniformity of the heater temperature is taken into account. Comparison of calculated and experimental data has showed the adequate description of the real process using the model. Analysis of identification parameters has given a satisfactory result.

Heat Conduction Problems in a Homogeneous Pipe with Inner Nonhomogeneous Coating

The paper deals with the analysis of nonhomogeneous inner coatings for a homogeneous pipe with respect of heat loss from the outer pipe surface. Two kinds of the coatings in the form of ring layers are considered: (1º) with the thermal properties changing continuously along the coating thickness (called the coating A), (2º) multilayered coatings with piecewise continuous thermal properties (called the coatings B). The analysis is connected with the stationary heat conduction problems. Some special cases of the coatings A and B are investigated. The obtained analytical results and the comparison of the coatings are presented.